10k!? Holy cow!
If you're moving your site, before you actually move anything, you need to do a few things (if you're also moving your domain to point to a new server)
- Set your domain's DNS TTL down to 5 minutes. Wait 24 hours for that change to propagate.
- During that 24 hours you can move your files over.
- Backup your site. Shut down the old site with a "moving" message. You might want to include "if you see this page, update your DNS since you're pointing to the old server"
- Change DNS/nameservers to the new host
- Wait 5 minutes, move your database over, as well as any files that may have changed
- Open your new site,
- Change TTL values back to the defaults/recommended
That should hopefully minimize your downtime. If your usage is high, I'd highly recommend going with a managed VPS provider; you'll like have the same issues on another shared host